There are many results for \(H\) -(super)magic graphs. Llado and Moragas [1]}
studied cycle-magic labeling of wheels, prisms, books, wind
mill graphs and subdivided wheels by using the technique of partitioning sets of integers. Ngurah et al. [2]} constructed
cycle-supermagic labelings for some families of graphs namely fans,
ladders, and books etc. For any connected graph \(G\) , Maryati et al. [3]},
proved that disjoint union of \(k\)  isomorphic copies of \(G\)  is a \(G\) -supermagic
graph if and only if \(|V(G)|+|E(G)|\)  is even or \(k\)  is odd. For a disconnected graph \(G,\)  having at least 2 vertices in its every components, the result was proved again by
Maryati et al. [4]}. For a positive integer \(k\) , they proved that (i) If \(kG\)  is \(G\) -magic, then \(|V(G)|+|E(G)|\)  is even or \(k\)  is odd and (ii) If \(|V(G)|+|E(G)|\)  is even or \(k\)  is odd, then \(kG\)  is \(G\) -supermagic.
For further detail, see the recent survey by Gallian [5]}.
